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Ivanka Milosevic
Milan Damnjanovic

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Ivanka Milosevic
Milan Damnjanovic

WSEAS Transactions on Biology and Biomedicine

Print ISSN: 1109-9518
E-ISSN: 2224-2902

Volume 14, 2017

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of WSEAS Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.

Maximally Efficient Symmetry Group Founded Diagonalization of Biophysical and Quantum Chemical Hamiltonians

AUTHORS: Ivanka Milosevic, Milan Damnjanovic

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ABSTRACT: We show that modified Wigner projector technique and generalized Bloch theorem approach yield maximally efficient diagonalization of the Hamiltonian of the large symmetrical systems. For the sake of illustration, we perform a case study of the simplified DNA molecule model and solve the energy eigenproblem analytically by using the unit symmetry cell (symcell) and the corresponding low-dimensional subspaces only. Relevant dynamical parameters are automatically obtained, enabling direct interpretation of the result. Effectiveness of the procedure is based on the two key points: (1) replacing infinite sums over the group elements by modified group projectors which are inherently determined by the group generators only; (2) reducing the dynamics of the system (from the infinite dimensional state space) to the low-dimensional symcell subspace, taking the benefit from the induced structure of the state space. Unlike the original Wigner projectors, the modified group projector technique is directly numerically applicable.

KEYWORDS: Deoxyribonucleic Acid (DNA), Symmetry,Wigner Group Projectors, Modified Group Projector Technique, Generalized Bloch Theorem, Electronic Bands, Eigenproblem, Inductive Spaces, Tight-binding Approximation


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[2] M. Damnjanovic and I. Milo ´ sevi ˇ c, Full sym- ´ metry implementation in condensed matter and molecular physics – Modified group projector technique, Phys. Rep. 581, 2015, pp. 1-43.

[3] M. Damnjanovic and I. Milo ´ sevi ˇ c,´ Line Groups in Physics - Theory and Applications to Nanotubes and Polymers, Springer, Berlin Heidelberg 2010

[4] N. W. Ashcroft AND N. D. Mermin, Solid State Physics, Holt, Rinehart and Winston, New York 1976

[5] J. D. Watson and F. H. C. Crick, A Structure for Deoxyribose Nucleic Acid, Nature 171, 1953, pp. 737-738.

[6] X. Zhao, J. Cui, Z. Li, X. Xu, Z. Shang, Y. Li, G. Wang, and R. Li, Symmetries of deoxyribonucleic acid (DNA) and related molecules J. Math. Chem. 2016, pp.1-33.

[7] J. C. Wang, Helical repeat of DNA in solution, PNAS 76, 1979, pp. 200-203.

[8] I. Milosevi ˇ c, A.Damjanovi ´ c and M. Damn- ´ janovic, Ch. XIV. In ´ Quantum Mechanical Simulation Methods in Studying Biological Systems, ed. D. Bicout and M. Field, Springer-Verlag, Berlin Heidelberg New York 1996

WSEAS Transactions on Biology and Biomedicine, ISSN / E-ISSN: 1109-9518 / 2224-2902, Volume 14, 2017, Art. #2, pp. 7-12

Copyright © 2017 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution License 4.0

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